Name: ______________________
Date: _________________
Investigation 4 Prime Time
National Library of Virtual Manipulatives – Sieve of Eratosthenes
Type in the following URL: http://matti.usu.edu/nlvm/nav/vlibrary.html
Click on “Number and Operations” Grades 6-8
Scroll to the bottom of the page and click on “Sieve of Eratosthenes”
Least Common Multiple Activity Sheet
Find the multiples of the following pairs of numbers and predict the common multiples for each
pair of numbers. Give the least common multiple between the pair. (Record your work in the
table below.)
Number
pair
Multiples
Common Multiples
Least Common
Multiple (LCM)
12
8
15
3
11
7
10
9
Adapted from Connected Mathematics©1998 by Michigan State University, Lappan, G., Fey, J., Fitzgerald, W.,
Friel, S., and Phillips, E. [ Investigation 4 – Prime Time]
NEIRTEC/ EDC 2002
Name: ______________________
Date: _________________
Investigation 4 Prime Time
There are many things in the world that happen over and over again in set cycles. Sometimes we
want to know when two things with different cycles will happen at the same time. Knowing
factors and multiples can help you solve such problems.
Example 1 –
A.) John goes to the park every 2 days. Chian goes to the park every 6 days. Which days will
they both be at the park?
Person
John
Chian
Days at the park
2, 4, 6, 8, 10, 12, 14, 16, 18…
6, 12, 18, …
Days in common
6, 12, 18…
B.) When is the soonest they will be in the park together?
C.) If John goes to the park every 7 days and Chian goes every 4 days when will be the next time
they will be in the park together?
D.) Explain how you found your answer.
Example 2 –
You and your friend go to the carnival that has both a large and a small Ferris wheel. You get on
the large Ferris wheel at the same time your friend gets on the small Ferris wheel. The ride
begins as soon as everyone is buckled in. Determine the number of seconds that will pass before
you and your friend are both at the bottom of the Ferris wheel together again….
A.) if the large wheel makes one revolution in 60 seconds and the small wheel makes one
revolution in 20 seconds.
B.) if the large wheel makes one revolution in 10 seconds and the small wheel makes one
revolution in 7 seconds.
Adapted from Connected Mathematics©1998 by Michigan State University, Lappan, G., Fey, J., Fitzgerald, W.,
Friel, S., and Phillips, E. [ Investigation 4 – Prime Time]
NEIRTEC/ EDC 2002
Name: ______________________
Date: _________________
Investigation 4 Prime Time
Example 3 –
Jose is shopping for party supplies. He finds a package of 10 plates, 16 napkins, and a package of
8 cups, What is the least number of packages of plates, napkins, and cups so that he has the
same number of each?
Example 4 – Create your own problem then find the solution. (use the back if necessary)
Adapted from Connected Mathematics©1998 by Michigan State University, Lappan, G., Fey, J., Fitzgerald, W.,
Friel, S., and Phillips, E. [ Investigation 4 – Prime Time]
NEIRTEC/ EDC 2002